S. K. Bogner

Model-independent low momentum nucleon interaction from phase shift equivalence

Abstract We present detailed results for the model-independent low momentum nucleon–nucleon interaction V low k . By introducing a cutoff in momentum space, we separate the Hilbert space into a low momentum and a high momentum part. The renormalization group is used to construct the effective interaction V low k in the low momentum space, starting from various high precision potential models commonly used in nuclear many-body calculations. With a cutoff in the range of Λ∼2.1 fm −1 , the new potential V low k is independent of the input model, and reproduces the experimental phase shift data for corresponding laboratory energies below E lab ∼350 MeV , as well as the deuteron binding energy with similar accuracy as the realistic input potentials. The model independence of V low k demonstrates that the physics of nucleons interacting at low momenta does not depend on details of the high momentum dynamics assumed in conventional potential models. V low k does not have momentum components larger than the cutoff, and as a consequence is considerably softer than the high precision potentials. Therefore, when V low k is used as microscopic input in the many-body problem, the high momentum effects in the particle–particle channel do not have to be addressed by performing a Brueckner ladder resummation or short-range correlation methods. By varying the cutoff, we study how the model independence of V low k is reached in different partial waves. This provides numerical evidence for the separation of scales in the nuclear problem, and physical insight into the nature of the low momentum interaction.

From low-momentum interactions to nuclear structure

We present an overview of low-momentum two-nucleon and many-body interactions and their use in calculations of nuclei and infinite matter. The softening of phenomenological and effective field theory (EFT) potentials by renormalization group (RG) transformations that decouple low and high momenta leads to greatly enhanced convergence in few- and many-body systems while maintaining a decreasing hierarchy of many-body forces. This review surveys the RG-based technology and results, discusses the connections to chiral EFT, and clarifies various misconceptions.

Similarity Renormalization Group for Nucleon-Nucleon Interactions

The similarity renormalization group (SRG) is based on unitary transformations that suppress off-diagonal matrix elements, forcing the Hamiltonian toward a band-diagonal form. A simple SRG transformation applied to nucleon-nucleon interactions leads to greatly improved convergence properties while preserving observables and provides a method to consistently evolve many-body potentials and other operators.

Is nuclear matter perturbative with low-momentum interactions?

Abstract The nonperturbative nature of inter-nucleon interactions is explored by varying the momentum cutoff of a two-nucleon potential. Conventional force models, which have large cutoffs, are nonperturbative because of strong short-range repulsion, the iterated tensor interaction, and the presence of bound or nearly-bound states. But for low-momentum interactions with cutoffs around 2 fm −1 , the softened potential combined with Pauli blocking leads to corrections in nuclear matter in the particle-particle channel that are well converged at second order in the potential, suggesting that perturbation theory can be used in place of Brueckner resummations. Calculations of nuclear matter using the low-momentum two-nucleon force V low k with a corresponding leading-order three-nucleon (3N) force from chiral effective field theory (EFT) exhibit nuclear binding in the Hartree–Fock approximation, and become less cutoff dependent with the inclusion of the dominant second-order contributions. The role of the 3N force is essential to obtain saturation, and the contribution to the total potential energy is compatible with EFT power-counting estimates.

Improved nuclear matter calculations from chiral low-momentum interactions

We present nuclear matter calculations based on low-momentum interactions derived from chiral effective field theory potentials. The current calculations use an improved treatment of the three-nucleon force (3NF) contribution that includes a corrected combinatorial factor beyond Hartree-Fock that was omitted in previous nuclear matter calculations. We find realistic saturation properties using parameters fit only to few-body data, but with larger uncertainty estimates from cutoff dependence and the 3NF parametrization than in previous calculations.

Low-momentum interaction in few-nucleon systems

The low-momentum nucleon-nucleon interaction

Towards a model independent low momentum nucleon nucleon interaction

{V}_{\text{low}\phantom{\rule{0.3em}{0ex}}k}

Low momentum nucleon-nucleon potential and shell model effective interactions

is applied to three- and four-nucleon systems. We investigate the

The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei

^{3}\mathrm{H}

Convergence in the no-core shell model with low-momentum two-nucleon interactions

,